First Response often only matters when there are agreements on the response time (like with an SLA). If you have any other reason for knowing this, you still have to define the definition of 'first response'. 
Having a custom field for this on task level and putting a flow behind it that updates that field on an update from an agent, could be one way to go, but you should really (re)consider the requirement itself. What will this customization resolve? Is it that important to know the first response on a task that is not subject to a service level?